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Monday 23 Mar 2015How Crossover Speeds Up Building-Block Assembly in Genetic Algorithms

Dr Dirk Sudholt - University of Sheffield

Harrison 170 15:00-16:30

Evolutionary algorithms use search operators like mutation, crossover and selection to "evolve" good solutions for optimisation problems. In the past decades there has been a long and controversial debate about when and why the crossover operator is useful. The building-block hypothesis assumes that crossover is particularly helpful if it can recombine good "building blocks", i. e. short parts of the genome that lead to high fitness. However, all attempts at proving this rigorously have been inconclusive. As of today, there is no rigorous and intuitive explanation for the usefulness of crossover. In this talk we provide such an explanation. For functions where "building blocks" need to be assembled, we prove rigorously that many evolutionary algorithms with crossover are twice as fast as the fastest evolutionary algorithm using only mutation. The reason is that crossover effectively turns fitness-neutral mutations into improvements by combining the right building blocks at a later stage. This also leads to surprising conclusions about the optimal mutation rate.

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